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When fabricating optical cantilever parts with single-point diamond turning (SPDT) technique, chatter phenomenon happens and degenerates the surface quality. This paper studies the chatter phenomenon and proposes a scheme to solve the problem. A kind of viscoelastic material is presented as the auxiliary supporter under the vibration location of optical cantilever parts to suppress chatter. Mirror surfaces can be generated and surface shape can be maintained after uninstalling the supporter because of the special features of viscoelastic material which acts like solid to enhance the rigidity of the cantilevers when cutting forces act on it and acts like liquid to avoid distortion of the surface shape during setting and unsetting the supporter. The effect of the viscoelastic material is discussed by virtue of finite element simulation on the basis of elasticity theory. Cutting experiments are carried out and the cutting forces as well as the surface quality with and without viscoelastic supporter are compared. The results show that chatter is suppressed effectively by using viscoelastic supporter, and surface roughness average (Ra) of around 5 nm is obtained on the whole surface with no obvious distortion on machined surface shape. [ABSTRACT FROM AUTHOR]